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CATEGORIES:Logic and Semantics Seminar (Computer Laboratory)
SUMMARY:Logics for Coalgebras - Alexander Kurz\, Universit
y of Leicester
DTSTART;TZID=Europe/London:20071130T140000
DTEND;TZID=Europe/London:20071130T150000
UID:TALK8356AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/8356
DESCRIPTION:Coalgebras for a functor _F_ generalize transition
systems. Using techniques from category theory\,
it is possible to study different classes of trans
ition systems uniformly in the parameter _F_. Coal
gebraic logic aims at extending this uniform appro
ach to logics of transition systems. In this talk\
, we will address the question how to associate to
any set-functor _F_ a corresponding logic\, toget
her with a complete calculus. This can be achieved
by associating to each _F_ a `dual' functor _L_ o
n Boolean algebras\, which encodes a modal logic f
or _F_-coalgebras.\n\nThis functorial view of a mo
dal logic leads to an elegant abstract\naccount of
modal logics for transition systems\, which we wi
ll review in this talk. In particular: a) In order
to explain the relationship\nbetween a functor _L
_ and its modal logic\, we introduce the notion of
a functor having a presentation by operations and
equations. The functors having a finitary such pr
esentation are characterized as the functors that
preserve sifted colimits. b) The classic theorems
of Jonsson-Tarski and Goldblatt-Thomason in Modal
Logic become theorems on algebras over the Ind- an
d Pro-completions of a category.\n\n[The results a
re from joint work with M. Bonsangue and with J. R
osicky]
LOCATION:Room FW11\, Computer Laboratory\, William Gates Bu
ilding
CONTACT:Sam Staton
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